On a Matrix Representation for Polynomially Recursive Sequences
Keywords: p-recursive, matrix representation, Galois theory
AbstractIn this article we derive several consequences of a matricial characterization of P-recursive sequences. This characterization leads to canonical representations of these sequences. We show their uniqueness for a given sequence, up to similarity. We study their properties: operations, closed forms, d'Alembertian sequences, field extensions, positivity, extension of the sequence to $\mathbb Z$, difference Galois group.